Question

If five $G.M.\text{'}s$ are inserted between $486$ and $\frac{2}{3}$ then the fourth $G.M$ will be

• A. $4$
• B. $6$
• C. $12$
• D. $-6$

Answer 1

The correct option is B

$6$

Finding the value of the fourth :

Let the five $GM\text{'}s$ be $G_1,G_2,G_3,G_4,$ and $G_5$

Then the series will be $486,G_1,G_2,G_3,G_4,G_5,2/3$

Here $a$$=$$486$

$7th$term $=2/3$

$\Rightarrow$ $a{r}^6=2/3$

$\Rightarrow$ $486r^6=2/3$

$\Rightarrow$ $r^6=1/3^6$

$\Rightarrow$ $r=1/3$

Fourth GM, $G_4=a{r}^4$

$=486{\left(1/3\right)}^4$

$=\mathbf{6}$

Hence option B is correct